یک روش خوشه بندی بر اساس رابطه فازی تعادلی برای مدیریت ارتباط با مشتری (CRM)

In real world, customers commonly take relevant attributes into consideration for the selection of products and services. Further, the attribute assessment of a product or service is often presented by a linguistic data sequence. To partition these linguistic data sequences of customers’ assessment on a product or service, a proper clustering method is essential and proposed in this paper. In the clustering method, the linguistic data sequences are presented by fuzzy data sequences and a fuzzy compatible relation is first constructed to present the binary relation between two data sequences. Then a fuzzy equivalence relation is derived by max–min transitive closure from the fuzzy compatible relation. Based on the fuzzy equivalence relation, the linguistic data sequences are easily classified into clusters. The clusters representing the selection preferences of different customers on the product or service will be the foundation of developing customer relationship management (CRM).

For the selection of an indicated product or service, customers often have to assess related attributes of the product or service. Commonly, the related attributes are so many and their important degrees are varied for different customers. Further, attributes ratings will stand for customers’ preferences that are presented with linguistic terms (Delgado et al., 1992 and Herrera et al., 1996), such as very poor (VP), poor (P), medium poor (MP), fair (F), medium good (MG), good (G) and very good (VG). Thus, a customer’s assessment on several attributes is expressed with a linguistic data sequence and many customers’ assessments on the attributes are shown with linguistic data sequences. To discover essential knowledge, linguistic data sequences of customers’ preferences have to be processed. In the information procedure, one of the most important technique is clustering (Bandyopadhyay and Maulik, 2002, Deogun et al., 1997, Dubes and Jains, 1988, Duda and Hart, 1973, Eom, 1999, Hirano et al., 2004, Kaufman and Rousseeuw, 1990, Khan and Ahmad, 2004, Krishnapuram and Keller, 1993, Kuo et al., 2004, Kuo et al., 2002, Kuo et al., 2005, Lee, 1999, Lee, 2001, MacQueen, 1967, Miyamoto, 2003, Paivinen, 2005, Pedrycz and Vukovich, 2002, Ralambondrainy, 1995, Wang and Lee, 2008 and Wu and Yang, 2002). For a given product or service, clustering methods can partition linguistic data sequences of customers’ assessments into clusters. The clusters respectively represent preferences of different customer groups in the product or service. Managers will develop related customer relationship management(CRM) and provide necessary assists for different customer groups according to their preferences. Thus, CRM is constructed on a clustering method. Through the above reason, clustering is a useful technique to develop CRM. In the past, lots of clustering methods (Bandyopadhyay and Maulik, 2002, Deogun et al., 1997, Dubes and Jains, 1988, Duda and Hart, 1973, Eom, 1999, Hirano et al., 2004, Kaufman and Rousseeuw, 1990, Khan and Ahmad, 2004, Krishnapuram and Keller, 1993, Kuo et al., 2004, Kuo et al., 2002, Kuo et al., 2005, Lee, 1999, Lee, 2001, MacQueen, 1967, Miyamoto, 2003, Paivinen, 2005, Pedrycz and Vukovich, 2002, Ralambondrainy, 1995, Wang and Lee, 2008 and Wu and Yang, 2002) were proposed. The clustering methods included cluster analysis, discriminant analysis, factor analysis, principal component analysis (Johnson & Wichern, 1992), gray relation analysis (Feng & Wang, 2000), and K-means ( Bandyopadhyay and Maulik, 2002, Khan and Ahmad, 2004, MacQueen, 1967, Ralambondrainy, 1995 and Wu and Yang, 2002), etc. Generally, cluster analysis, discriminant analysis, factor analysis and principal component analysis are often applied in classic statistical problems, such as large sample or long-term data. On the contrary, gray relation analysis and K-means are preferred to deal with small sample or short-term data. Thus, an appropriate method of clustering will be selected by the data pattern. Commonly, most of the previous clustering methods are often utilized in crisp values, no matter how data belong to large sample, small sample, long-term, or short-term. However, a clustering method in this paper has to partition linguistic data sequences into clusters to present the preferences of different customer groups. That is to say, the clustering method will partition data under impression, subjectivity and vagueness. Based on the concept, the method is proposed and expressed below. First, linguistic terms are transferred into fuzzy numbers in the clustering method. Then the method will construct a fuzzy binary relation between any two fuzzy data sequences. The fuzzy binary relation is rooted in the similarity of two data sequences and satisfies compatible relation. However, the elements of different clusters may overlap as the fuzzy binary relation merely satisfies compatible relation for partitioning. To solve the overlap problem, some additional mechanisms (Lee, 1999, Lee, 2001 and Wang and Lee, 2008) are essential on the compatible relation. For instance, Wang and Lee (2008) proposed additional mechanisms to resolve the ties, but the mechanisms may be complex and difficult in computation. Generally, a simpler mechanism is max-min transitive closure (Lee, 1999 and Lee, 2001), being one of most popular methods, which is often utilized on compatible relation. In this paper, we utilize the max–min transitive closure as the additional mechanism to transform fuzzy compatible relation into fuzzy equivalence relation. Then fuzzy data sequences are partitioned into clusters by the equivalence relation. After clustering, the intra-relations relations will be high, whereas the inter-cluster relations are low. In short, fuzzy data sequences are from linguistic data sequences and partitioned into clusters by fuzzy equivalence relation for an indicated product or service. One cluster stands for a customer group having similar preferences to the product or service on attributes. After grasping these attribute preferences of different clusters, CRM will be developed on the varied attribute preferences. For the sake of clarity, mathematical preliminaries are presented in Section 2. The fuzzy compatible relation and equivalence relation are proposed in Section 3. Finally, an empirical example of CRM concerning the application of credit cards is illustrated in Section 4.

In this paper, we propose a clustering method based on fuzzy equivalence relation. By the fuzzy equivalence relation, the clustering method can partition fuzzy data sequences into clusters easily, and the sequences with similar preferences will be clustered into a cluster. Thus, the clustering method is a technique of developing CRM. To demonstrate the method’s ability, we illustrate an empirical example to partition customers into different preference groups on applying for credit cards. In addition, the clustering is based on the five factors, i.e. fees, credit, function, fame and image, and promotion in this example. However, factors’ number is merely five, and may bring the partitioning difficulty because many sequences are indiscernible on the five factors. On this situation, the five factors can be restored as the previous criteria, and then the sequences are easily partitioned according to the 15 criteria. That is to say, the clustering method can easily develop CRM of applying for credit cards on different respects.